Law of Sine and Law of Cosine

Front

What is the Law of Sines?

Back

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. It can be expressed as: a/sin(A) = b/sin(B) = c/sin(C).

Front

What is the Law of Cosines?

Back

The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. It is expressed as: c² = a² + b² - 2ab*cos(C).

Front

What type of triangle can the Law of Sines be applied to?

Back

The Law of Sines can be applied to any triangle, including acute, obtuse, and right triangles.

Front

What type of triangle can the Law of Cosines be applied to?

Back

The Law of Cosines can be applied to any triangle, including acute, obtuse, and right triangles.

Front

What is the criteria for using the Law of Sines?

Back

The criteria for using the Law of Sines are: SSA (Side-Side-Angle), ASA (Angle-Side-Angle), and AAS (Angle-Angle-Side).

Front

What is the criteria for using the Law of Cosines?

Back

The criteria for using the Law of Cosines are: SSS (Side-Side-Side) and SAS (Side-Angle-Side).

Front

If angle A = 50 degrees and angle B = 60 degrees, what is angle C?

Back

Angle C = 180 - (A + B) = 180 - (50 + 60) = 70 degrees.

Front

How do you find the length of a side using the Law of Sines?

Back

To find the length of a side using the Law of Sines, use the formula: a/sin(A) = b/sin(B) = c/sin(C) and solve for the unknown side.

Front

What is the relationship between the angles and sides in a triangle?

Back

In a triangle, the larger the angle, the longer the opposite side. Conversely, the smaller the angle, the shorter the opposite side.

Front

What is an ambiguous case in the Law of Sines?

Back

An ambiguous case occurs in the SSA configuration where two different triangles may be possible, or no triangle may exist.